This paper considers the effect of time-dependent lower boundary wave forcing on the internal variability found to appear spontaneously in a stratosphere-only model when the forcing is perfectly steady. While the time-dependent forcing is found to modulate the internal variability, leading in some cases to frequency locking of the upper-stratospheric response to the forcing, the temporal and sp...

In 1962 Paul Cohen invented set-theoretic forcing to solve the independence problem of continuum hypothesis. It turns out that forcing is quite powerful tool and it has applications in many branches of mathematics. In 1970s Abraham Robinson extended Cohen’s forcing to model theory and developed finite forcing and infinite forcing. In this term paper we study Robinson’s finite forcing and relate...

If two models of a first order theory are isomorphic then they remain isomorphic in any forcing extension of the universe of sets. In general, however, such a forcing extension may create new isomorphisms. For example, any forcing that collapses cardinals may easily make formerly non-isomorphic models isomorphic. Certain model theoretic constraints on the theory and other constraints on the for...

since the properly religious training of children is the main concern of many religious families in modern era, so the importance and necessity of this research is clear. this paper does research on different dimensions of children's prayer and their forcing to prayer by parents and criterions and range of this forcing according to time of validity and parents' authorized and unauthor...

In my lecture at the 2011 Congress on Logic, Methodology, and the Philosophy of Science in Nancy, France, I spoke on an additional axiom of set theory — the Proper Forcing Axiom — which has proved very successful in settling combinatorial problems concerning uncountable sets. Since I have already written a exposition on this subject [43], I have decided to address a broader question in this art...

The purpose of this paper is to present some results which suggest that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. What will be proved is that a form of simultaneous reflection follows from the Set Mapping Reflection Principle, a consequence of PFA. While the results fall short of showing that MRP implies SCH, it will be shown that MRP implies that if SCH fails fir...

Forcing is a technique that was discovered by Cohen in the mid 20th century, and it is particularly useful in proving independence results. The process involves adding new, generic elements to your universe and using them to prove a result. In many applications this is encapsulated by the addition of suitable axioms, often these are Forcing Axioms. One of the first such principles is known as M...

In order to present this result, we approach it by proving some preliminary theorems about different forcings which capture the main ideas in a simpler setting. For the entirety of the notes we work with an increasing sequence of large cardinals 〈κn | n < ω〉 with κ =def supn<ω κn. The large cardinal hypothesis that we use varies with the forcing. A recurring theme is the idea of a cell. A cell ...